Question

(2 questions please help medal given to best answer)
In this pair of similar trapezoids, what is the length of side GF?
A. 2
B. 20
C. 24
D. 36
In the two similar trapezoids below, HE = 20, what is DA?
A. 10
B. 20
C. 30
D. 40

Answer 1

@mathstudent55 can you please help out

Answer 2

What side in trapezoid ABCD does side GF correspond to?

Answer 3

CB

Answer 4

Correct.
In similar polygons, the lengths of corresponding sides are in the same ratio.
The ratio of the lengths of GF to CB is 10x to 30

Answer 5

Now we need another set of two corresponding sides that we are given both lengths, either as numbers or expressions.

Answer 6

HG and DC

Answer 7

Exactly.
in the same order we did above, the ratio of the lengths is:
56 to 42x

Answer 8

Now we set these two ratios equal to each other and solve for x.

Answer 9

10x to 30 = 56 to 42x

\(\dfrac{10x}{30} = \dfrac{56}{42x} \)

Answer 10

Now we solve the proportion for x.

Answer 11

We cross multiply:

\(10x \times 42x = 30 \times 56\)

\(420x^2 = 1680\)

Divide both sides by 420:

\(x^2 = 4\)

\(x = 2\)

Answer 12

Since side GF has length 10x, what is 10 * 2 = ?

Answer 13

20

Answer 14

You got it!

Answer 15

so 2 is the answer for question number 1 and 40 is the answer for question 2 right

Answer 16

The answer for the first question is 20.

Answer 17

ah sorry my bad yes its is 20

Answer 18

and question 2 is 40 right?

Answer 19

Look again at GF and CB.
GF is 20 and CB is 30.
CB is 1.5 times the length of GF.
The larger trapezoid has all sides 1.5 times the side of the sides of the smaller trapezoid.

Answer 20

If HE is 20, then since DA corresponds to HE, DA must be 1.5 times the length of HE.

Answer 21

oh so its 20 * 1.5 =30

Answer 22

Correct.